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Coding for the additive white Gaussian noise (AWGN) channel that also introduces an unknown carrier phase rotation is considered in this work. A simple model that captures the phase dynamics is one, where the unknown carrier phase is considered constant over a block of N symbols, and independent from block to block. In this work, LDPC codes in conjunction with pilot symbols are considered. In particular, a single pilot symbol of specified power is inserted in the beginning of each block of length N, in order to aid the joint estimation and decoding process. As expected, the presence of a pilot symbol implies an inevitable loss in the transmitted power, resulting in a trade-off between the power allocated between the pilots and the coded bits, and the quality of the joint estimation and decoding process.